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Re: How atrocious is "center of gravity"?



On Fri, 14 Apr 2000 16:35:15 -0400 THOMAS SANDIN <sandint@NCAT.EDU>
writes:
"Center of mass" is a mass-weighted average position. "Center
of gravity" is a gravitational force-weighted average position (I
could
have said "weight-weighted"). If g is essentially constant over the
system, the center of gravity is essentially at the center of mass.
Then we
can do without the term "center of gravity".
However, here's an example where both terms are useful.
Suppose a meter stick is in orbit about the earth. If the stick is NOT

horizontal, particles of the stick closer to the earth have a bit more

gravitational force than equal-mass particles farther from the earth.
As a result,
the center of gravity is below the center of mass. Since we can treat
the entire weight of the stick as acting at its center of gravity, the
weight of the stick exerts a torque about the stick's center of mass,
tending to align the stick's long axis with the earth's gravitational
field.
This torque can be used to orient satellites (my memory is
that the jargon is something like gravitational-gradient orientation).
Allowed to swing freely, the stick will oscillate back and forth about
its
alignment position. It's not hard to get a good approximation for
its period using centers of gravity--I did so many years back when the
AAPT was looking for experiments to be done in orbit.
Tom Sandin


I suspect that the gravitational force difference between
the ends of a tilted meter stick in space would be much
to small to measure. However if it is significant, what
about the differential losses in moisture from different
parts of the meter stick as the moisture evaporates
in the vacuum of space? Also, should we consider
the differential pressures of the sunlight at the
ends of the meter stick?? Why...or why not??

Herb Gottlieb from New York City
(Where no two wooden meter sticks are exactly the same length)